Fresnel zone beam scanning array



3 m '2 5 CROSS REFERENCE SEARCH mm March 31 1970 R. w. RUBEN 3,504,368

FRESNEL ZONE BEAM SCANNING ARRAY Filed Oct. 5, 1966 2 Sheets-Sheet l FOCAL DISTANCE/ \i /2 l4 UNIFORMLY ILLUMINATED OB=OA= RADIUS OF APERTURE APERTURE FIG. 2

INVENTOR.

ROBERT W. RUBEN ZKQMW ATTORNEY March 31, 1970 Filed Oct. 5, 1966 A PROJECTED ZONES BECOME ELLIPSES RECEIVE PHASE DELAY OF H ELEMENT R. W. RUBEN FRESNEL ZONE BEAM SCANNING ARRAY 2 Sheets-Sheet 2 FIG.3

TRANSMIT PHASE DELAY OF H" ELEMENT INVENTOR.

ROBERT W. RUBEN MWLM ATTORNEY 3,504,368 Patented Mar. 31, 1970 US. Cl. 343--701 2 Claims ABSTRACT OF THE DISCLOSURE An antenna system having an aperture comprised of a planar array of :ariable gain amplifier-antenntl. elements geometrically arranged so that selected Fresnel'lzone patterns may be forined on the aperture. by contiolling the distribution of ghin among the antenna elements. Each antenna element fconsists of a spiral antenna hailing an integrally imbedded. tunnel diode amplifier. A primary feed horn is placed at thev focal distance from the aperture, and a direct current bias distribution networl lis usedtq selectively control the gain of the amplifier-antennas.so as to provide beiim steering by controlling the formation and variation of Fresnel zone patterns on the aperture.

This inveiitioii' relates generally to aperture antennas -and, more particularly, to electronic beam teering of whereby desired radiation characteristics af achieved.

from an arrayof elementary antennas by corftrolling .the amplitude and -phase excitation of each eleriient of the array. Optical antennas are considerably mori l simple to' implement than arrays, which require a coinplex feed structure and associated phase shifting devices; however, arrays provide 'distinct advantages in precisiofi of control and versatility;.:--. The objects of the present infvention are achieved, in part, by an approach which combines ithe advantages of 'antennas designed by array theory and those based on geometrical optics. r

A known antenna that combines array theory and geometrical optics was introduced by D. G. Berry, R. G. Malech and W. A. Kennedy in a paper entitled, The Reflectarray Antenna, published in the 1963 issue of the IEEE Transactions on Antennas and Propagation." The Refiectarray comprises an aperture that is characterized by a surface impedance and a primary radiator that illuminates this surface. The amplitude and phase of the fields reflected from the surface at any point are determined by the surface impedance at that point. To provide beam steering, the necessary phasing or realization of surface impedance is accomplished by using either a dielectric slab of variable dielectric constant or a waveguide array with a series of switching diodes placed in the waveguide elements at appropriate intervals. The waveguide array provides an important practical advantage over the dielectric slab in that a variety of radiation patterns may be produced in rapid sequence by electronic means; however, this approach also has a number of drawbacks, the most obvious being the large physical size and weight of a structure of open-ended waveguideelemerits. The waveguide Reflectarray presents further disadvantages in that the switching diodes cause loss in the system, and relatively large numbers of diodes are requit-ea to accomplish beam steering.

With an awareness of the foregoing limitations disadvantages of the prior art, applicant has a general object of the present invention to provide an improved nitefd States Patent Office high gain antenna system with the capability of electronic beam steering.

A primary object of the invention is to provide a simplified and relatively compact means of implementing efiicient, precise beam scanning of a large aperture antenna. f

A further object is to provide a lossless beam forming method for large aperture scattering and receiving arrays.

Another object of the invention is to provide a large aperture array in which electronic beam steering and high gain are provided, without the necessity of a complex feed structure and associated phase shifting devices.

Still another object is to provide a large aperture antenna, with electronic beam scanning capability, which is relatively compact and lightweight.

Briefly, these objects are attained "by employing an aperture adapted to form Fresnel zone patterns, placing a feed antenna at the focal point of the aperture and providing beam steeringiby electronically controlling the formation and variation of Fresnel zone patterns on the aperture. In particular, {the aperture comprises an array of variable gain antennafelements geometrically arranged so that selected Fresnel zone patterns may be formed on the aperture by controlling the distribution of gain among the antenna elements.

In a preferred embodiment, the aperture or scattering surface is comprised of a planar array of amplifierantenna elements, each at which consists of a printed circuit spiral antenna having an integrally imbedded tunnel diode amplifier. A primary feed horn is placed at the focal distance from the aperture, and a direct current bias distribution network is used to selectively control the gain of the amplifier-antennasL' Other objects, features and advantages of the invention will become apparent and its construction and operation better understood from the following detailed description, taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a pictorial representation of an antenna according to the invention? FIG. 2 is a diagram of-the Fresnel zone construction for normal incidence;

FIG. 3 is a diagram of the Fresnel zone construction for oblique incidence;

FIG. 4 is a diagram illustrating beam position with respect to the antenna aperture;

FIG. 5 is a diagram illustrating the phase relationship for beam forming with a linear array;

FIG. 6 is a pictorial representation of an amplifier-antenna element useful in the antenna of FIG. 1; and

FIG. 7 is a schematic diagram of a bias network for the amplifier-antenna element of FIG. 6.

The present invention, which shall be referred to as a Fresnel zone beam scanning array, is illustrated in FIG. 1 and comprises a circular aperture 10 including amplifier-antenna elements 12, and a primary feed horn 14 positioned at the focal point of the aperture by conventional support means, not shown. The amplifier-antenna elements are uniformly spaced across the entire aperture to provide a planar electromagnetic wave reflecting surface.

Beam scanning is efiected by selectively controlling the gain of amplifier-antenna elements in particular zones of apertures 10 as determined by the aperture geometry and direction of the scanned beam. More specifically, the gain distribution among the elements is employed to form Fresnel zone patterns on the aperture. Only elements in alternate Fresnel Zones that are additive at the focal point are contributing; hence, the amplifier outputs of the remaining elements are appropriately controlled by varying the respective direct current bias voltages. Typically, the alternate zone amplifier-antennas are biased on, while the remainder are biased off. In this way, incoming radi ation within the beamwidth of an element can be focussed in the central feed 14 simply by forming the appropriate Fresnel zone pattern on the surface or aperture 10. In the transmit mode, the operationwould be reversed, with the radiation from feed 14 being reflected by the scattering surface and formed as abeam in the appropriate direction by the selected Fresnel zone pattern.

The location of contributing Fresnel zones can be determined from geometrical optics. It is well known from diffraction theory that the field disturbance at a point P from a uniformly illuminated aperture can be calculated by subdividing the aperture into half-period, or Fresnel, zones. The contributions to the field at point P from adiacent Fresnel zones are 180 out of phase and nearly cancel. The shape and position of these zones depend upon the incident angle of the energy received. Construction of these zones can be easily derived using Fresnels zone construction techniques.

NORMAL INCIDENCE Consider a plane wave incident on a circular aperture from a direction perpendicular to the plane. In other words, the aperture is uniformly illuminated. From a point P, which is on the axis to the center of the plane, spheres of radii D+n \/2 are constructed so they intercept the aperture; D=focal distance, and )\=wavelength. FIG. 2 illustrates the Fresnel zones resulting from this contruction technique.

'The division of the wavefront has the following geometric properties:

-(1) In passing from one zone boundary to the next, the distance to the point P increases by M2; and

.(2) The outer boundary of the 21 zone has a radius given by r.. =nx1)+ n=1, 2, 3.

and if D which is the case,

REV (2) Thus, the Fresnel zones are defined by concentric circles with radii r given above. The area of the n zone is given by A =1r(r r )1rD)\ (3) so that all zones have approximately the same area. At

P, the field is made up of thecontributions from the Fresnel zones which can be represented by where; E is the amplitude of the n zone; and

du=D+ (2W1 is the average distance to P from the n zone. Note again that (d -d )=(a' d )=)\/2, so that at any time t, the sum of the zones may be written as so hat Therefore, E is dependent only on the factor (1+cos o which varies slowly for small n. It can be seen that, by enhancing the odd numbered zones with amplifier-antenna elements, the field E will increase from E 1 assuming =E +l toa new value of d= 1+ 3+ 5+ n where the new E (for n odd) are also increased by the gain ofthe amplifiers, and the negative E values (for n even) are comparatively insignificant.

OBLIQUE INCIDENCE The next point to consider is the Fresnel pattern for angles .of incident radiation othergthan normal to the aperture. Assume incident radiation is a plane wave at angle 0, and all initial phases of the elements are at 0". In reference to the circular Fresnelaperture that is illuminated with a plane wave at an' angle 0, the reflected wave can be considered to have emanated from a uniformly illuminated aperture that is oriented at angle 0, or the "aperture center can be considered to have shifted off axis'as shown in FIGURE 3.

From the geometry in FIG. 3, the new projected centers of the Fresnel zones are located at 0 where 0 =0+D tan 0 (7) for beam steering in one linear direction. These projected zones are seen to be ellipses with the major axis reater than the minor axis by 1/ cos 0 In general, the minor axis is given by 2 2 r =r \nDcos0l- (9) where 0 is the scan direction, and n, as before, is the zone number.

For beam steering in both the 0 and directions as shown in FIG. 4 (and FIG. 1), can'be seen that, if the coordinate system is rotated about the z axis by the angle the same situation would occur as was discussed under scanning in the 0 direction only.'

Using the familiar transformation of coordinates under rotation of axis, the new primed coordinates (x, y) can be expressed in terms of (x, y,

x=x cos +y sin qb, and, (10) y=y cos sin qb. (11) In general, the expression for an ellipse is given by :0)v (I l 0) Combining Equations 10, 11 and 12 yields an expression that can be used to determine the location and size of the Fresnel zones required to focus energy at P for all scan position (0, 5.

Noting that the major axis of the ellipse is always along the x axis and the minor axis along the y axis, and substituting the proper values into Equation 12 yields:

n x no. 1 [nDA cos (H- [nDA cos 0+ Where Simplifying (13) leads to:

cos

which expresses the general equation for the Fresnel zones on a plane circular 'a'perture as a function of (0,

In FIG. 1, feed horn v s positioned at the above mentioned focal point P, which is located on the z-axis at a focal distance D from apefi ture 10, the z-axis being normal to the aperture plane at its center. The interelement spacing, h, of amplifier antenna elements 12 depends on many factors including element size, desired radiation pattern characteristics and co onsiderations; a reasonably practical spacing has be found to be from one-half to a full wavelength betweencenters. It is to be noted,,hoW.- ever, that although antenna elements 12 are illustrated as being uniformly distributed in a planar grid pattern, other geometrical arrangements; such as linear array or nonuniform distributions, may be used, as warranted by the application and cost considerations, providedthe arrangement allows the desired Fresnel patterns to be formed bn the aperture. Typically, a computer would be used to control the gain distribution among the antenna elements and xy sin cos tan (i=- thereby provide Fresnel: zone beam steering, the inputs to the computer being coordinates of the elements on the planar aperture and the above derived -ge'n'eral Equation 14. For the receive mode, an acquisition and tracking radar could be used tof'provide 0 and 95 inputs to the computer. ;.1

The radiation patternspf the array may be computed in the general manner illllstrated below for the case of a linear Fresnel zone array. t The primary radiator ',(feed horn 14) illuminates the array aperture with a spherical wave as shown in FIG.

5. The phase on receive to be,

on the 1 element can be-shown so the total phase G,, of the i element is the sum of receive and transmit phases or G.= (D-w/D +(ih) +ih sin a) (15) The far field contribution due to the summation of these elements is then given by I E E; A; EXP JTGi] appropriate wl'ife A, is the amplitude of the element pattern, and only th elements that are contained within the appropriate Fre'nel zones are contributors. The above summation is eq alent to the value of E expressed in Equation 6.

In a preferred embodiment of the invention, aperture 10 (lFIG. 1) is a fiat scattering surface comprising a rigid or fielrible dielectric sheet 16 on which is supported an arraylof amplifier-antenna elements 12, each of which consisfi1 ofa printed circuit spiral antenna having an integra y imbedded tunnel" diode amplifier, as shown-in FIG. 6. Dielectric sheet 16 also supports a printed circuit direct c rrent bias distribution network, as will be described E more detail hereinafter, to selectively control the gain f the amplifier-antennas. The construction and operation of this integrated tunnel diode amplifier-spiral antenna and the biasing method associated therewith is fully described in copending patent application Ser. No. 501,144, filed Oct. 22, 1965, and assigned to the assignee of the present invention. This construction particularly advantageous in that it provides an antenna: structure of planar configuration which is easily fabricated, light in weight, compact and capable of broadband operation at high microwave frequencies. j-

Referring to FIG. 6, one arm 1-8 of the spiral antenna is etched on one side of the dielectric sheet 16, and the second arm 20 is etched on the other side of the dielectric. A narrow printed circuit center conductor 18a extends from the terminal of arm 18 and is aligned with arm 20 so as to form a microstrip transmission line wherein arm 20 functions as a ground plane. A pill-type tunnel diode 22, such as a Sylvania D5061 or a Microwave Associates MA4652A, is imbedded int o and electrically connected across the transmission'line, between the center conductor 18a and the ground platle (arm 20), at a selected distance along the line. The center conductor extending between the terminal of arm 18 aftd the diode may.be shaped and dimensioned as a step type or tapered impedance transformer to provide an impedance match bet-ween the diode circuit and the antenna. An open or short eircuited transmission line stub for circuit tuning is provided by appropriate termination of the center conductor, at a selected distance beyond the diod 'Jinto an open circuit (as in FIG. 6) or by a shortin pa" imbedded in the transmission line. The bias olt'age 'for the tunnel diodeamplifier is applied across the transmission line, in a manner.tdi bedescribedhereinaf a pill-type bias resistor 24 is-imbedded infarid iconne; across the transmission line at' the voltage null generated by the tuning circuit, or reasonably close thereto, so as to provide low frequency stabilization.

. In order to provide direct current bias or modulation to the amplifier of this integrated unit and yet overcome the isolation, narrowband operation and complex constructional problems of prior art techniques, the properties of the frequency independent antenna :are utilized. The "various portions of this type of antenna are resonant at different frequencies, and by connecting the source of bias voltage to a portion of the antenna which is resonant below the active microwave band of operation, isolation off'the bias and microwave circuits is obtained. In the case of the frequency independent spiral antenna, the

. source of bias or modulating voltage is con ricted across the ends 18b and 20a of antenna arms 18 an;,20, respectively. That is, tunnel diode 22 is biased by a voltage source connected across the transmission line 18a/ 20 and fed through the spiral arms of the antenna. The outer extremities of the spiral are resonant at a low frequency, and any change of impedance (discontinuity) at the ends of the spiral due to thebias connections is greatly reduced at the spiral input, which is resonant at a higher microwave frequency, f Further, the arrrlglength of the spiral is sufficiently long so that most of thi energy (fed to the spiral input at f;) is radiated before the discontinuity at the end of the arm is reached. Any energy reflected at the end of the arm is then radiated with an opposite polarization sense and results .in an ellipticity of the antenna polarization. It is possible to' get a rough measure of the reflection by the ellipticity of the antenna polarization. For example, if the ellipticity is 2 db, the reflection back at the antenna terminals 'is down 30 db from the input. This circuit is a broadband as the bandwidth of the antenna.

Thus, by feeding the bias via the ends of the antenna arms, thereby utilizing the resonant properties of a frequency independent antenna, the generation of standing waves and other discontinuities due to the bias source is minimized and amplifier stability is maintained, The tech; nique is compatible with the printed circuit amplifierantenna package and the array bias distribution network about to be described. All bias leads can be imprinted along with the antenna, and isolation is achieved without the use of auxiliary networks.

In order to selectively control the gain of the amplifierantenna elements, the bias distribution network connections are arranged as illustrated in the schematic circuit diagram of FIG. 7. One of the spiral antenna arms, in this instance arm 20, is connected to ground through; its end terminal 201:, while the end terminal of the other spiral antenna arm, in this instance end 18b, is controllably connected through a switch 26 to a source of positive direct current voltage +V, represented by terminal 28. Preferably, the bias circuit paths are conductors etched on dielectric sheet 16, and switch 26 is a transistor or diode adapted to be controlled by an electric signal. A number of array network arrangements may be found suitable. For example, the end terminal 20a of each amplifier-antenna element could be connected through a grid network to a common ground, and each end terminal 18b might be separately connected via respective controlled switches to a common voltage source +V. On the other hand, a plurality of voltage sources may be employed. Further, if the application allows, groups of the amplifier-antenna elements may be connected via a common controlled switch to a direct current voltage source. Typically, the control signals for opening and closing the bias voltage switches for selected elements in particular zones of the aperture would be generated by a computer, pursuant to calculations based upon the element locations and the above derived general equation for Fresnel zones (-11) as a function of the desired beam steering angles and It will be apparent from the foregoing that the present invention provides a simplified and relatively compact means of implementing efficient and precise electronic beam steering of a large aperture antenna. The gain of the antenna system is particularly enhanced by the use of amplifier-antenna elements in Fresnel zone patterns on the aperture. The beam forming method described employs an essentially lossless phase control technique, without the necessity of a complex feed structure and associate phase shifting devices. In addition, the further advantages of small size and light weight are achieved by the use of integrated amplifier-antenna elements.

It is to be understood that although there has been described what are now considered to be preferred embodiments of the invention, modifications falling within the scope and spirit of the invention will occur to those skilled in the art. For example, antennas other than a feed horn may be employed as the primary radiator; other types of gain variable antenna elements may be used, rather than the described amplifier-antennas; and, means other than a bias network may be employed for controlling the distribution of gain among the antenna elements. It is intended, therefore, that the invention not be limited to what has been specifically illustrated and described except as such limitations appear in the appended claims.

What is claimed is:

1. An antenna system including: an aperture which comprises a planar array of integrated amplifier-antenna elements; a feed antenna positioned at the focal point of said aperture; and a direct current bias distribution network operative to selectively control the gain of said amplifier-antenna elements; each of said amplifier-antenna elements being of planar configuration and comprising a sheet of dielectric material, a printed circuit spiral antenna having a first arm etched on one side of said dielectric sheet and a second arm etched on the other side of said dielectric sheet, a printed circuit center conductor extending from the terminal of said first arm and aligned with said second arm so as to form a transmission line wherein said second arm functions as a ground plane, and a tunnel diode imbedded in said transmission line.

2. An antenna system in accordance with claim 1 wherein said bias distribution network is arranged to controllably connect a source of voltage across the ends of the first and second arms of each of said spiral antennas for biasing said tunnel diode to operate as an amplifier in said transmission line, said arms providing isolation between said bias source and said amplifier.

References Cited UNITED STATES PATENTS 2,986,734 5/1961 Jones et a1. 343-7S4 3,259,902 7/1966 Malech 343-754 3,189,907 6/1965 Buskirk, 343910 3,392,393 7/1968 Spitz' 343754 ELI LIEBERMAN, Primary Examiner U.S. Cl. X.R. 343754, 895 

